Today I was trying to find the value of 2^i, not exact value though but something in the form of a formula. After 3 hours I ended up with a generalized formula for n^i. I am attaching an image and a pdf file of my work.
I run a Facebook Group called not just tiny-c Programming Group. A member recently posted the above problem. This is actually a very old problem but we were encouraged to give it a shot without looking it up. The original problem was this: graph the above equation. For "extra credit" we were encouraged to solve it for rational numbers. An obvious solution is x=y. Also, 2^4=4^2. It turns out there are infinitely many rational numbers that solve this equation. I wrote a computer program in C which approximately solved our equation. I populated a table with the x,y values it generated into desmos and got a pretty good graph. Actually, you can just put the equation itself into desmos and get the exact graph. But the rationals was too tough for me. I eventually did the research and got the answer. Very, very interesting. I watched blackpenredpen's videos on this. I doubt this rational problem would have enough general interest to make a video on this but ... you never know.